Imported OBJ will not move to grid
Because its already snapped to the grid.

To explain: OBJ is a mesh-only format, therefor there is no object center. Just geometry and the object center is always (0, 0, 0), so there is no snapping to do.

To do what I think you're asking, you can have blender calculate a new origin (in the toolbox Origin -&gt; Origin to Geometry), then you can snap the objects to the grid.

You may also want to split the mesh by loose parts before doing this though OBJ may be already split up, depending on the import options.